Theorem:- ∑ anzn is a power series and ∑ nanzn - 1 is the power series obtained
by differentiating the first series term by term.
Then the derived series has the same radius of convergence as the original series.
See the attached file.
Radius of Convergence of the Power Series
This solution is comprised of a detailed explanation of the radius of convergence of the function. The radius of convergence of the power series are determined.